An Iterative Method for Finding the Least Solution to the Tensor Complementarity Problem

Shui-Lian Xie (), Dong-Hui Li () and Hong-Ru Xu ()
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Shui-Lian Xie: South China Normal University
Dong-Hui Li: South China Normal University
Hong-Ru Xu: Jiaying University

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 1, No 6, 119-136

Abstract: Abstract In this paper, we are concerned with finding the least solution to the tensor complementarity problem. When the involved tensor is strongly monotone, we present a way to estimate the nonzero elements of the solution in a successive manner. The procedure for identifying the nonzero elements of the solution gives rise to an iterative method of solving the tensor complementarity problem. In each iteration, we obtain an iterate by solving a lower-dimensional tensor equation. After finitely many iterations, the method terminates with a solution to the problem. Moreover, the sequence generated by the method is monotonically convergent to the least solution to the problem. We then extend this idea for general case and propose a sequential mathematical programming method for finding the least solution to the problem. Since the least solution to the tensor complementarity problem is the sparsest solution to the problem, the method can be regarded as an extension of a recent result by Luo et al. (Optim Lett 11:471–482, 2017). Our limited numerical results show that the method can be used to solve the tensor complementarity problem efficiently.

Keywords: Tensor complementarity problem; Z-tensor; Least solution; Sparsest solution; Monotone convergence; 90C33; 15A72; 65N12 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s10957-017-1157-5

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